MHB Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?

  • Thread starter Thread starter TheDougheyMan
  • Start date Start date
  • Tags Tags
    Theorem Value
TheDougheyMan
Messages
2
Reaction score
0
I have a continuous function h(x) and the inequality h(b)<=0<=h(a). Can I apply IVT?
 
Physics news on Phys.org
Well, what are the hypotheses of the IVT? Are they satisfied in your case?
 
Ackbach said:
Well, what are the hypotheses of the IVT? Are they satisfied in your case?
Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.
 
TheDougheyMan said:
Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.

Exactly right. So you can conclude that there is a $c \in (a,b)$ (I'm assuming $a<b$) such that $h(c)=0$.
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
View full post »

Similar threads

I Uniform convergence of difference quotient in higher dimensions
Replies
1
Views
2K
I Understanding an argument in Intermediate Value Theorem
Replies
5
Views
2K
I Exercise 2.23 in Folland's real analysis text
Replies
2
Views
2K
I Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)
Replies
2
Views
2K
A Question about different statements of Picard Theorem
Replies
0
Views
2K
MHB Intermediate Value Theorem ....Silva, Theorem 4.2.1 .... ....
Replies
3
Views
3K
MHB Understanding Theorem 3.4: Mean Value Theorem & Cauchy Riemann Equations
Replies
2
Views
1K
MHB When is the Maximum Angle for Viewing a Tower from an Airplane?
Replies
12
Views
1K
MHB Differentiation on R^n ....need/ use of norms ....
Replies
4
Views
1K
I Differentiation on R^n ....need/ use of norms ....
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top